PHS COVID-19 : Preparing for winter

Prathiba

22/10/2021

Scope of Analysis



Daily Cases:


People tested positive

Cases based on Neighborhood (Local Authority)

Vaccination

As of 30th September in Scotland,

Daily number of Vaccination

Percentage Coverage of Vaccination by age group

Cumulative total number of Vaccination

COVID-19 Hospitalizations and Deaths

Hospital admissions

Deaths (based on COVID-19 confirmed)



COVID-19 Hospitalization Projection: ARIMA Model(p,d,q):

The Automated Regression Integrated Moving Average technique is used for the COVID-19 Time Series Data.

Based on statistical parameters (lower AIC, RMSE and p-value), an ARIMA (3,1,2) model has been chosen for Hospital projections.

Fitting the ARIMA (3,1,2) with existing data

Projection of Hospitalization

COVID-19 Deaths Projection ARIMA Model(p,d,q):


Based on statistical parameters (lower AIC, RMSE and p-value)
ARIMA(2,1,3) with lag = 1 has been chosen.

Fitting the models with existing data

Projection of new Deaths based on 4 models

Key Points

Summary:

Projections:

Future Proposal:













Thank you !!!













Questions !!!













Appendix

Auto Regression Integrated Moving Average: ARIMA (p, d, q) Model

Hospitalization Projection :

  1. Original Series Vs First Order Difference

  1. Augmented Dicky Fuller Test (Finding d)

##            Data Dickey_Fuller   p_value
## 1      Original     -1.088300 0.9208883
## 2 First-Ordered     -7.507224 0.0100000

  1. Estimate the Parameters (Finding p and q)

Auto Regression Integrated Moving Average: ARIMA (p, d, q) Model (contd..)

  1. Build the ARIMA model

Manual ARIMA

## 
## ========================================================
##                 ARIMA(3,1,2)  ARIMA(3,1,0)  ARIMA(0,1,2)
## --------------------------------------------------------
## ar1                0.92 ***     -0.26 **                
##                   (0.09)        (0.09)                  
## ar2               -0.58 ***     -0.23 *                 
##                   (0.11)        (0.09)                  
## ar3               -0.31 ***     -0.16                   
##                   (0.09)        (0.09)                  
## ma1               -1.35 ***                   -0.28 **  
##                   (0.03)                      (0.09)    
## ma2                1.00 ***                   -0.17 *   
##                   (0.04)                      (0.08)    
## --------------------------------------------------------
## AIC             1002.61       1027.69       1025.20     
## AICc            1003.35       1028.03       1025.40     
## BIC             1019.39       1038.87       1033.58     
## Log Likelihood  -495.31       -509.84       -509.60     
## Num. obs.        121           121           121        
## ========================================================
## *** p < 0.001; ** p < 0.01; * p < 0.05

Automated ARIMA (lag = 1)

## 
## ============================
##                 ARIMA(3,1,2)
## ----------------------------
## ar1                0.94 *** 
##                   (0.10)    
## ar2               -0.56 *** 
##                   (0.11)    
## ar3               -0.25 *   
##                   (0.10)    
## ma1               -1.44 *** 
##                   (0.05)    
## ma2                0.94 *** 
##                   (0.04)    
## ----------------------------
## AIC              983.97     
## AICc             984.71     
## BIC             1000.70     
## Log Likelihood  -485.99     
## Num. obs.        120        
## ============================
## *** p < 0.001; ** p < 0.01; * p < 0.05

Auto Regression Integrated Moving Average: ARIMA (p, d, q) Model (contd..)

  1. Check the diagnostics

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(3,1,2)
## Q* = 33.437, df = 5, p-value = 3.082e-06
## 
## Model df: 5.   Total lags used: 10

  1. Fitting the ARIMA model with the existing data

Auto Regression Integrated Moving Average: ARIMA (p, d, q) Model (contd..)

  1. Hospitalization Projection using ARIMA (3,1,2)

Based on the (AIC),(RMSE), and (MAPE) , it’s been identified that the model ARIMA(3, 1, 2) with lag = 1 seems reasonable.